Is having a bi directional message queue a design smell?

I have an architecture with 1 backend server and multiple frontend servers.

The frontend servers are connected in a bi-directional (web sockets) connection to clients so they can send messages to clients.

The frontend and backend are connected through a message bus. There is one queue for frontend to backend messages and another queue for backend to frontend messages.

For example, when a client requests an operation, the frontend sends the request to the backend and acknowledges the client the request was sent.

Sometimes, when the backend finishes handling a request, it sends a status message to the frontend who forwards it to the client that requested the operation.

I've never seen anything similar. Usually the communications only go one way - from frontend to backend.

I'm worried, am I doing something bizarre?

I came up with this architecture because of the bi-directional nature of web sockets. This way the server can notify clients as soon as a request is processed.